2.3 Solid-state transformer

The last formulation describes in functional way the mathematical model for a

An electrical disturbance is characterized by the deviations that it produces to the nominal voltage, current, or frequency conditions. These fluctuations can result in failure or abnormal operation on the system. These perturbations can be noticed as wave deformations affecting magnitude or frequency mainly. This effect is of uttermost importance in electrical utilities since they face the task to provide highquality energy by regulation, in addition to balance generation and demand with adequate levels of electromagnetic compatibility that allows proper operation of

Some equipment with nonlinear components, such as power electronic converters, electric arc devices, and others, cause problems usually related to electromagnetic interference (EMI). These disturbances cause a loss of performance in

distribution lines. However, one of the most significant problems in addition to the performance degradation is the deterioration on the quality of the voltage sine wave, superimposing periodic or transient disturbances. This phenomenon

jeopardizes the appropriate operation of electronic, computer, and communication

Given the aforementioned problems, there is a need to formulate a model that could handle analysis and simulation. Table 2 shows the mathematical model and

Assume i tð Þ¼ I<sup>1</sup> cosðω0t þ θ1Þ

where α>1 and 0:01 ≤t ≤0:6 s

where 0 < α < 1 and 0:01 ≤t ≤0:6 s

I<sup>1</sup> cosð Þ ω0t þ θ<sup>1</sup> , t<sup>1</sup> ≤t 0 , t<sup>1</sup> ≤t ≤t<sup>2</sup> I<sup>1</sup> cosð Þ ω0t þ θ<sup>1</sup> , t ≥t<sup>2</sup>

I<sup>1</sup> cosð Þ ω0t þ θ<sup>1</sup> , t<sup>1</sup> ≤t αI<sup>1</sup> cosð Þ ω0t þ θ<sup>1</sup> , t<sup>1</sup> ≤t ≤t<sup>2</sup> I<sup>1</sup> cosð Þ ω0t þ θ<sup>1</sup> , t ≥t<sup>2</sup>

I<sup>1</sup> cosð Þ ω0t þ θ<sup>1</sup> , t<sup>1</sup> ≤t αI<sup>1</sup> cosð Þ ω0t þ θ<sup>1</sup> , t<sup>1</sup> ≤t ≤t<sup>2</sup> I<sup>1</sup> cosð Þ ω0t þ θ<sup>1</sup> , t ≥t<sup>2</sup>

<sup>h</sup>¼<sup>1</sup>Ih cosð Þ <sup>h</sup>ω0<sup>t</sup> <sup>þ</sup> <sup>θ</sup><sup>h</sup> (17)

(14)

(15)

(16)

i tðÞ¼

i tðÞ¼

i tðÞ¼

8 >>< >>:

8 >>< >>:

8 >>< >>:

where 0:01 ≤t ≤0:6 s

most conventional loads and unnecessarily overload in transmission or

representation of the electrical disturbances analyzed in this chapter.

Perturbance Representation Mathematical model

Harmonics i tðÞ¼ <sup>∑</sup>NH

Electrical waveform disturbance mathematical model.

nonlinear load.

electrical equipment.

Momentary interruption

systems.

Swell

Sag

Table 2.

124

2.2 Electrical waveform disturbances

Research Trends and Challenges in Smart Grids

The SST allows isolation between medium- and low-AC voltage sides as any conventional transformer. Additionally, it allows the isolation and clearance of faulty conditions from both sides, as well as anomalies encountered in the AC or DC sides. Its DC link is highly attractive for the integration of photovoltaic energy, storage systems with uninterrupted power supply devices, or even future local DC grids. In order to accomplish all these features, its topology has several stages of power electronic blocks depending on the functionalities required. Thus, the SST can be designed depending on the type of application [23]. As a key technology in the implementation of the smart grid, its topology will heavily depend on the end user consumption and the integration and coordination features required. Some of these requirements are shown in Table 3.

As the modular arrangement of the SST depends on the grid requirements, several topologies have been proposed in the literature. Generally, the energy can be processed in three main stages: rectification, the same level AC-AC or DC-DC conversion, and inversion. Some of the available solutions to these stages are shown in Table 4. To provide a wider classification system for the SST, the level of modularity can be determined with respect to power flow direction, connection to three-phase systems, and connection to the medium-voltage level [24].


### Table 3.

Various functional requirements for the SST.


#### Table 4.

Typical power electronics topology for the SST stages.

A typical configuration of a SST consists of [25]:


Stage Electrical circuit Mathematical model in

MCHBC iLiðÞ¼ <sup>s</sup> Vgrid ð Þ�<sup>s</sup> mVroutð Þ<sup>s</sup>

DABC <sup>Δ</sup>PDAB

Solid-State Transformer for Energy Efficiency Enhancement

DOI: http://dx.doi.org/10.5772/intechopen.84345

ILP iLf d

Table 5.

MCHBC

DABC

ILP

Table 6.

127

Description of each controller SST stage.

Description of each mathematical model SST stage.

Stage Driver

frequency domain s

<sup>Δ</sup><sup>ϕ</sup> <sup>¼</sup> VHVDCVLVDC

ECLVDC <sup>¼</sup> <sup>1</sup>

Vf d�Vo d <sup>¼</sup> <sup>1</sup>

iLf d ð Þs Vo d ð Þ<sup>s</sup> <sup>¼</sup> Zo

iLf qð Þs Vo q ð Þ<sup>s</sup> <sup>¼</sup> Zo

iLf q Vf q�Vo q <sup>¼</sup> <sup>1</sup>

ECHVDCð Þs iLið Þ<sup>s</sup> <sup>¼</sup> Vgrid ð Þ<sup>s</sup>

RiþsLi (18)

<sup>2</sup><sup>s</sup> (19)

<sup>2</sup>πfsLDAB (20)

<sup>s</sup> PDAB (21)

Rf <sup>þ</sup>Lf <sup>s</sup> (22)

Rf <sup>þ</sup>Lf <sup>s</sup> (24)

<sup>1</sup>þsZoCf (23)

<sup>1</sup>þsZoCf (25)


To understand in a better way the SST topology, Figure 3 is presented. Focusing on the control system, it is divided into three stages: (1) multilevel

cascade H bridge converter (MCHBC), which facilitates the conversion from AC to DC; (2) dual-active-bridge (DABC) DC-DC converter that allows the regulation of the energy in the low-voltage link capacitor and indirectly the DC voltage; (3) a three-phase inverter in series with a low-pass filter (inverter low-pass filter, ILP), which takes DC input wave and transforms it into AC without any distortion in the waveform. Table 5 shows the description of the electrical circuit and mathematical model of each stage of the SST.

Figure 3. Topology of the SST.
